L11a350

(Knotscape image)

See the full Thistlethwaite Link Table (up to 11 crossings).

Planar diagram presentation	X_12,1,13,2 X₈₄₉₃ X_18,14,19,13 X_22,20,11,19 X_20,7,21,8 X_6,21,7,22 X_4,15,5,16 X_14,5,15,6 X_16,10,17,9 X_2,11,3,12 X_10,18,1,17
Gauss code	{1, -10, 2, -7, 8, -6, 5, -2, 9, -11}, {10, -1, 3, -8, 7, -9, 11, -3, 4, -5, 6, -4}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-\frac{t(2)^3 t(1)^3-3 t(2)^2 t(1)^3+4 t(2) t(1)^3-2 t(1)^3-3 t(2)^3 t(1)^2+8 t(2)^2 t(1)^2-8 t(2) t(1)^2+4 t(1)^2+4 t(2)^3 t(1)-8 t(2)^2 t(1)+8 t(2) t(1)-3 t(1)-2 t(2)^3+4 t(2)^2-3 t(2)+1}{t(1)^{3/2} t(2)^{3/2}}$ (db)
Jones polynomial	$q^{11/2}-4 q^{9/2}+9 q^{7/2}-15 q^{5/2}+19 q^{3/2}-21 \sqrt{q}+\frac{21}{\sqrt{q}}-\frac{18}{q^{3/2}}+\frac{12}{q^{5/2}}-\frac{8}{q^{7/2}}+\frac{3}{q^{9/2}}-\frac{1}{q^{11/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$- z 7 a -1 + 3 a z 5 -4 z 5 a -1 + z 5 a -3 -3 a 3 z 3 + 8 a z 3 -8 z 3 a -1 + 2 z 3 a -3 + a 5 z -5 a 3 z + 6 a z -6 z a -1 + 2 z a -3 + a 5 z -1 - a 3 z -1$ (db)
Kauffman polynomial	$-2 a 2 z 10 -2 z 10 -4 a 3 z 9 -12 a z 9 -8 z 9 a -1 -3 a 4 z 8 -6 a 2 z 8 -14 z 8 a -2 -17 z 8 - a 5 z 7 + 9 a 3 z 7 + 25 a z 7 + z 7 a -1 -14 z 7 a -3 + 10 a 4 z 6 + 32 a 2 z 6 + 22 z 6 a -2 -9 z 6 a -4 + 53 z 6 + 4 a 5 z 5 + a 3 z 5 - a z 5 + 26 z 5 a -1 + 20 z 5 a -3 -4 z 5 a -5 -10 a 4 z 4 -32 a 2 z 4 -10 z 4 a -2 + 7 z 4 a -4 - z 4 a -6 -40 z 4 -6 a 5 z 3 -11 a 3 z 3 -14 a z 3 -21 z 3 a -1 -11 z 3 a -3 + z 3 a -5 + 2 a 4 z 2 + 9 a 2 z 2 + 2 z 2 a -2 -2 z 2 a -4 + 11 z 2 + 4 a 5 z + 5 a 3 z + 4 a z + 5 z a -1 + 2 z a -3 + a 4 - a 5 z -1 - a 3 z -1$ (db)

The coefficients of the monomials

t r q j

are shown, along with their alternating sums

χ

(fixed

j

, alternation over

r

). The squares with yellow highlighting are those on the "critical diagonals", where

j -2 r = s + 1

j -2 r = s -1

, where

s =

1 is the signature of L11a350. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = 0$	$i = 2$
$r = -6$	${\mathbb Z}$
$r = -5$	${\mathbb Z}^{2}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -4$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{2}$	${\mathbb Z}^{3}$
$r = -3$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{5}$	${\mathbb Z}^{5}$
$r = -2$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{7}$	${\mathbb Z}^{7}$
$r = -1$	${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{11}$	${\mathbb Z}^{11}$
$r = 0$	${\mathbb Z}^{11}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{11}$
$r = 1$	${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{10}$	${\mathbb Z}^{10}$
$r = 2$	${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{9}$	${\mathbb Z}^{9}$
$r = 3$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = 4$	${\mathbb Z}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = 5$	${\mathbb Z}_2$	${\mathbb Z}$